Question: $J$ $K$ $L$ If: $ JL = 74$, $ KL = 5x + 2$, and $ JK = 3x + 8$, Find $KL$.
Explanation: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {3x + 8} + {5x + 2} = {74}$ Combine like terms: $ 8x + 10 = {74}$ Subtract $10$ from both sides: $ 8x = 64$ Divide both sides by $8$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $KL$ $ KL = 5({8}) + 2$ Simplify: $ {KL = 40 + 2}$ Simplify to find ${KL}$ : $ {KL = 42}$